I have 2 new features in mind I at least would like to have for correspondence games.
The first is being able to change the game title. This would change the title only for you. Also the title would be nice to have when you view the game above the player info. The tab/window title could also contain the game title/player names.
An other one is to be able to make personal notes for a game. It could work as an extra chat option (so it would be: chat/malcovitch/note).